math

The distance between towns M and N is 280 km. A car and a lorry travel from M to N. 
The average speed of the lorry is 20 km/h less than that of the car. The lorry takes 1 h 10 min more than the car to travel from M and N. 
(a) If the speed of the lorry is x km/h, find x 
(b) The lorry left town M at 8: 15 a.m. The car left town M later and overtook the lorry at 12.15 p.m. Calculate the time the car left town M.

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  1. speed of lorry ---- x km/h
    speed of car ----- x+20 km/h

    time for the car = 280/(x+20)
    time for lorry = 280/x

    280/x - 280/(x+20) = 70/60
    divide by 70
    4/x - 4/(x+20) = 1/60
    times 60x(x+20), the LCD
    240(x+20) - 240x = x(x+20)
    240x + 4800 - 240x = x^2 + 20x
    x^2 + 20x - 4800 = 0
    (x - 60)(x + 80) = 0
    x = 60 or x is a negative

    the speed of the lorry is 60 km/h

    b) at the time of overtaking, the lorry had gone for
    4 hrs, thus it had gone 240 km
    for the car to go those same 240 km would have taken 240/80 hrs or 3 hrs.
    So just "backup" 3 hrs from 12:15

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